Polyadic Supersymmetry
We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the <i>n</i>-ary sigma matrices define...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/11/4/125 |
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| Summary: | We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the <i>n</i>-ary sigma matrices defined in earlier work. In this way, polyadic analogs of supercharges and Hamiltonians take the cyclic shift block matrix form, and they are different from the <i>N</i>-extended and multigraded SQM. While constructing the corresponding supersymmetry as an <i>n</i>-ary Lie superalgebra (<i>n</i> is the arity of the initial associative multiplication), we have found new brackets with a reduced arity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>m</mi><mo><</mo><mi>n</mi></mrow></semantics></math></inline-formula> and a related series of <i>m</i>-ary superalgebras (which is impossible for binary superalgebras). In the case of even reduced arity <i>m</i>, we obtain a tower of higher-order (as differential operators) even Hamiltonians, while for <i>m</i> odd we obtain a tower of higher-order odd supercharges, and the corresponding algebra consists of the odd sector only. |
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| ISSN: | 2218-1997 |